My soil is consists of a 6"-12" layer of topsoil over solid clay. While my property has a decent slope, it is poorly drained due to the clay forcing all of the water to stay in the top few inches of the yard.

I can and will provide drainage around the oven, but am going back and forth on the foundation for my 42" oven.

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I built a 600sq ft deck (adjacent to the oven area) and hand dug 21 2' x 4' rectangular holes 3' deep to accomodate footers for the sonotube deck supports. I used 21 footers due to very poor load bearing capacity of clay soil. The deck has not moved (2.5 years old).

I am not sure if I should dig down below frost level (about 3') and pour a traditional foundation and build a block wall to hold the base slab, or simply excavate down 1' or so and build a well drained gravel base to pour the slab directly onto.

The floating slab would be much easier, but if I don't get the base well compacted and drained, then frost heave could be an issue. On the other hand, a foundation hole will allow water to migrate downwards toward the footer but never drain away (solid clay). The resulting water could form ice lenses that would attempt to attach to (and heave) the concrete block foundation walls. I suppose all of the cores would need to be concrete filled, or concrete foundation walls poured with smooth sides. Costly, to say the least.

When I say poorly drained, I can dig a 3' deep post hole and fill it with a garden hose and it will never drain. No kidding...

Thoughts based on my soil conditions? Any of you have similar conditions?

I would go with the floating slab. A lot less work. My second choice would to go with three sonotube piers.

I had actually considered sonotube piers to support the lower slab, but the weight is simply too much for the bearing surface that clay provides. I would need 4 or 5 very substantial footers or sonotubes and that is as much trouble as just digging the entire footer.

I am rather sure that the flaoting slab will rise and fall with the frost and with enough thickness and rebar, it should not crack. The bigger concern is it shifting or becoming unlevel over time?

This is the most stressful part of this project for me... choosing the proper foundation for my ground soil and drainage conditions.

I am in MN with soil like yours--heavy clay with almost no topsoil. I went with four pier footings under/tied to the lower slab and a bit heavier on the rebar. I probably also have closer to 7-8" slab thickness vs. 6". It sits on a few inches of sand and gravel. Three winters, so far, so good. I have no idea if that is at all related to the presence of the footings, but every other (4") slab I have at the house that is directly on uncorrected soil--driveway, patio and sidewalk, all frost heave in the winter, despite 2' rebar grid and being pinned into the frost walls of my house with same.
I'm not sure what is more fun--digging and moving clay or watching it destroy $20K worth of flatwork.
I agree that deciding what to do about the foundation was the worst and most stressful part. And I also agree that the possibility of a floating slab bearing load but becoming unlevel over time would be a huge bummer. Fixing that would be a project.

I know of one other pompeii in MN that was built on a floating slab. I think that one has 2" of EPS or iso under the slab, for what I'm not sure. And I haven't heard how it's weathering...

I do plan on pouring close to 8" with heavy rebar. I did not pour my walk and driveway so am not sure how well the soil was prepped or how much drainage was provided, but they certainly do frost heave every winter. My driveway heaves so much that I was unable to open the door on the previous shed, indicating at least 1" of movement. The 4 slab driveway is also drifting apart and has been ever since we moved in about 6 years ago.

I think even if it is well drained below the slab (the gravel base) the caly underneath is saturated and expands when it freezes. I am not sure there is any way around it.

Insulating such a slab is a waste of time, as the insulation will be at equillibrium with the ground in a matter of days, so I am also not sure why they did that. I can see a vapor barrier to keep the wood storage area dry...

So you put tubes on the 4 corners and tied them to the slab with rebar? How big are the footers for the tubes?

I did not use tube forms. I find that with digging by hand, a post hole digger makes a perfect earth formed hole and I can never find small enough tube form anyway. So I suppose my cylindrical holes are roughly 6-7" dia. and I did try to mushroom them at the bottom to approximate a true footing and a bit more anchoring. Four piers total with a few sticks of rebar in each. I left one stick long on each footer and then bent it over to tie into the slab grid.

For comparison, around here, doing any outdoor flatwork the right way would mean digging out and replacing down about 2'. I have no idea how/if that would have changed things for my slabs--I'm sure it would have helped but, as you say, you've still got water stuck under the drainage base with nowhere to go.
If that's your sticking point I guess you could consider drain tiling around it. It'd mean more digging but be cheap and easy after that.

I did try to mushroom them at the bottom to approximate a true footing and a bit more anchoring.

I agree that tubular footings are more or less useless (Alternative to concrete block foundation) unless they are flared at the bottom. They make specific forms for casting these in combination with the sonotubes, but of course that means a lot more excavation.

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I use tube forms to ensure that my piers are smooth walled to prevent ice from grabbing on to them. After the deck and shed (21 for the deck, 9 for the shed) and 15 or so odd fence posts, i am pretty quick about digging a 2' by 3' hole with a shovel and posthole digger I suspend the tube form (using a simple frame) about 10" off of the bottom and fill the tube and hole in one shot. If you only knew how many 80# bags of concrete I have hand mixed over the last 3 years!

I can put a drain tile around the oven base, but can only get it down maybe 1' and still keep enough pitch to get the water to drain down away from the patio.

I am still a bit concerned about the weight per pier and the limited bearing surface that it will rest on. Brick, slab, and finish stone are going to come in at maybe 10,000 - 15,000 pounds.

That is ~3,000 pounds per pier so even with a 2' x 2' base, you are 750 pounds per square foot!

Your success has given me at least some hope that the slab may be an option. Maybe I can go down 1' or so and backfill with compacted stone over geotextile cloth. The cloth will prevent the stone from migrating downward into the clay and the drain tile will keep it somewhat drained.

When all is said and done, I suppose most engineers would have me dig a traditional foundation and build or pour a wall.

I may have just talked myself into sonotube footers... lets say worst case 15,000 pound oven. With 5 legs, (one in the middle) that would be 3,000 pounds per leg. With a 2' x 2' footer the load would be 750 pounds per square foot.

The bearing capacity of clay is listed someplace in the neighborhood if 2000 PSF. So it would appear that the legs would not pile in any further as long as they were below the frost line.

I suppose the next question would be concerning the intregity of the slab resting on 5 points of contact. I guess extra thick and extra rebar will come into play, begging the question if it would just be easier and safer to pour a traditional footer and build walls?

What about the weight distribution? If the load above is spread via the hearth slab to the U or square perimeter block stand, is a central pier in your foundation really going to have any benefit?
A full depth perimeter footing and foundation wall would be a box without anything in the center, so it's not clear to me why a central pier is helpful in the sonotube situation. Basically all it's doing is supporting the middle of the foundation slab itself.
I'm certainly not the expert here...just wondering out loud.

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